Diskretne slučajne varijable i primjene

undergraduate thesis

• Title (english): Discrete random variables and applications
• Author: Alena Đogić
• Mentor: Erna Begović Kovač (mentor)
• Committee member: Miroslav Jerković (predsjednik povjerenstva)
• Committee member: Monika Šabić Runjavec (član povjerenstva)
• Committee member: Vanja Kosar (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2024-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj završni rad bavi se tematikom diskretnih slučajnih varijabli te njihovom primjenom u statistici i inženjerstvu. U prvom dijelu završnog rada definiramo diskretne slučajne varijable i njihove osnovne karakteristike kao što su funkcija gustoće vjerojatnosti, funkcija distribucije vjerojatnosti, očekivana vrijednost, varijanca i standardna devijacija. U drugom dijelu rada analiziramo nekoliko važnih distribucija, uključujući Bernoullijevu, binomnu, Poissonovu, negativnu binomnu, geometrijsku te hipergeometrijsku distribuciju. Svaka distribucija prikazana je različitim primjerima i grafičkim prikazima.
Rad omogućuje bolje shvaćanje i razumijevanje diskretnih slučajnih varijabli, te njihovo korištenje.

Abstract (english)

This final thesis deals with the topic of discrete random variables and their application in statistics and engineering. In the first part of the thesis, we define discrete random variables and their fundamental characteristics such as probability density function, probability distribution function, expected value, variance and standard deviation. In the second part of the thesis, we analyze several important distributions, including Bernoulli, binomial, Poisson, negative binomial, geometric and hypergeometric distribution. Each distribution is illustrated with various examples and graphical representations.
The thesis aims to provide a better understanding of discrete random variables, and their use.

• Keywords: slučajne varijable; Bernoullijeva distribucija; binomna distribucija; Poissonova distribucija; negativna binomna distribucija; geometrijska distribucija; hipergeometrijska distribucija; Excel
• Keywords (english): random variables; Bernoulli distribution; binomial distribution; Poisson distribution; negative binomial distribution; geometric distribution; hypergeometric distribution; Excel
• Language: croatian
• URN:NBN: urn:nbn:hr:149:169319
• Study programme: Title: Materials Science and Engineering - Undergraduate study; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka kemijskog inženjerstva (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka kemijskog inženjerstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-11-17 18:43:02